With recent advances in three-dimensional data acquisition techniques, computer aided design (CAD) techniques and graphics hardware, an increasing amount of three-dimensional models spread over various archives, such as the Internet and specific databases. On the other hand, designing of high fidelity three-dimensional models is both very costly and time consuming. Therefore, effective exploitation of existing models becomes important, but it is difficult to retrieve useful models from the huge amount of collections. Many efforts have been made by scholars to find efficient three-dimensional model retrieval approaches.
Various methods have been so far proposed for three-dimensional model retrieval, and they can be broadly divided into two classes: key words based retrieval method and content based retrieval method. In the former kind of methods, the three-dimensional model is described in the semantic level and the feature of the model is expressed with a series of descriptive words, such as size, material, color or category. They are applicable in early stage when the size of collections of three-dimensional models is small. In the latter kind of methods, content of the model itself is taken into consideration during the model retrieval process. With sharp increase in the number of the models, more and more attention is focused on content based retrieval techniques. The currently available content based retrieval methods can be classified into three categories: feature vector based method, topology based method and two-dimensional images based method.
In feature vector based methods, a feature vector is used to describe a three-dimensional object. Shape distribution is the best known method of this kind. Refer to Non-patent document 1 for details of the shape distribution method. Methods of this kind have very high efficiency in feature extraction and model comparison. However, the retrieval precision is not satisfactory because the feature vector is relatively simple and the information of the model is not precisely described. Nonetheless, these methods may be integrated into other methods as a pre-classifier due to their simplicity and efficiency.
In topology based retrieval methods, the structure of the three-dimensional model is described using tree or graph, and the comparison of two models is accomplished by matching two trees or graphs; refer to Non-patent document 2 for details. Topological structure provides intuitive and important information of the shape of a three-dimensional model, and such feature is invariant of affine transformation. However, topology is sensitive to tiny changes in the model and topology matching of trees and graphs is too time-consuming, and these defects restrict the application of such kind of methods.
In two-dimensional images based retrieval methods, a series of two-dimensional images are generated based on three-dimensional models, and the three-dimensional models are compared by comparing the corresponding two-dimensional images. Among these methods, the light field descriptor as described in Non-patent document 3 and the characteristic view as described in Non-patent document 4 are most widely applied model retrieval methods based on two-dimensional images.
In the method described in Non-patent document 3, 10 light field descriptors are used to express the features of a three-dimensional model, while each light field descriptor consists of the features of 10 images. The models are compared through comparison among these light field descriptors. In the generation of two-dimensional images based on a three-dimensional model, a regular dodecahedron is placed at the center of a model, and twenty vertices of the regular dodecahedron are used as viewpoints to generate twenty binary images via quadrature projection, wherein two images taking two vertices at opposite locations as viewpoints are identical, so that ten images are retained, and one light field descriptor is generated based on these ten images. Different images can be obtained by rotating the regular dodecahedron, so as to obtain different light field descriptors. In the method of Non-patent document 3, ten light field descriptors are generated, and two light field descriptors are compared by accumulating distances between matched images. Altogether one hundred images should be applied in the process of obtaining the ten light field descriptors.
In the method based on characteristic view as described in Non-patent document 4, a regular icosahedron is placed at the center of a three-dimensional model, and polygons of the regular icosahedron are segmented to obtain eighty uniformly distributed polygon. The centers of these eighty polygons are then taken as viewpoints to obtain eighty initial views via quadrature projection. Representative views are selected from the initial eighty views for each three-dimensional model. Subsequently on the basis of Bayesian probability theorem, a representative view corresponding to the query image are found out from all the representative views of the models to thereby calculate similarities between the query and the database models.
According to some synthetic documents, retrieval methods based on two-dimensional images can get better retrieval results as compared with retrieval methods based on feature vector and retrieval methods based on topology; refer to Non-patent documents 5 and 6 for details.
However, the aforementioned methods based on two-dimensional images are restricted for practical application due to their huge number of images and hence time consumption in the process of feature extraction and model comparison.    Non-patent document 1: R. Osada, R. Funkhouser, T. Chazelle: Shape distributions. ACM Transactions on Graphics, 21(5), 807-832 (2002).    Non-patent document 2: M. Hilaga, Y Shinagawa, T. Kohmura, T. L. Kunii: Topology matching for fully automatic similarity estimation of 3D shapes. Proceedings SIGGRAPH, 203-212 (2001).    Non-patent document 3: C. Ding-Yun, T. Xiaopei, S. Yute, O. Ming: On visual similarity based 3D model retrieval. Proceedings of European association for Computer Graphics, 22(3), 223-232 (2003).    Non-patent document 4: T. F. Ansqry, J. Vandeborre, M. Daoudi: A framework for 3D CAD models retrieval from 2D images. Annual of telecommunications technologies and tools for 3D imaging. Vol. 60 (11-12), 2005.    Non-patent document 5: P. Shilane, P. Min, M. Kazhdan, T. Funkhouser: The Priceton shape benchmark. Proceedings of the international conference on Shape modeling, 167-178 (2004).    Non-patent document 6: N. Iyer, S. Jayanti, K. Ramani: An engineering shape benchmark for 3D models. Proceedings of ASME IDETC/CIE, 24-28 (2005).